Elliptic curve isogeny class 2178.5-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-2178.5-b
• Conductor: 2178.5
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-2}) \)

Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).

Elliptic curves in class 2178.5-b over \(\Q(\sqrt{-2}) \)

Isogeny class 2178.5-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
2178.5-b1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -12\) , \( -81\bigr] \)
2178.5-b2	\( \bigl[1\) , \( 1\) , \( 1\) , \( -2\) , \( -1\bigr] \)
2178.5-b3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -155 a + 68\) , \( 272 a - 1205\bigr] \)
2178.5-b4	\( \bigl[1\) , \( 1\) , \( 1\) , \( 155 a + 68\) , \( -272 a - 1205\bigr] \)
2178.5-b5	\( \bigl[1\) , \( 1\) , \( 1\) , \( -22\) , \( -49\bigr] \)
2178.5-b6	\( \bigl[1\) , \( 1\) , \( 1\) , \( -352\) , \( -2689\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 4 & 2 & 2 & 2 & 4 \\ 4 & 1 & 8 & 8 & 2 & 4 \\ 2 & 8 & 1 & 4 & 4 & 8 \\ 2 & 8 & 4 & 1 & 4 & 8 \\ 2 & 2 & 4 & 4 & 1 & 2 \\ 4 & 4 & 8 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph